Nonlinear Stability and Vibration Analysis of Flexible Spacecraft Solar Arrays under Thermally Induced Deformations within the Thermal Flutter Regime during the Penumbra Phase

This study develops a nonlinear analytical model of a spacecraft with flexible solar arrays to investigate complex vibration phenomena occurring within the thermal flutter regime, particularly during the satellite’s transition through the penumbra phase. The model captures dynamic behaviors driven by transient thermal gradients and structural flexibility key contributors to self-excited oscillations in orbit. Two major nonlinear phenomena are examined: limit cycle oscillations (LCOs) self-sustained periodic motions arising under subcritical thermal conditions and internal resonance, which emerges within the flutter velocity range and strongly influences modal interactions. Special attention is given to the Hubble Space Telescope (HST), where nonlinearities stem from large elastic deformations and thermally induced loads and torques. A combined analytical–numerical approach is adopted, incorporating nonlinear dynamic modeling and time-domain simulations. The focus is on the penumbra phase, where the thermal wave propagation velocity is less than the speed of solar radiation. The system’s coupled bending–bending–twisting motion equations include quadratic and cubic nonlinearities. Through model reduction, a tractable set of nonlinear ordinary differential equations is derived. Using the method of multiple scales (MMS), internal resonance conditions are analytically identified to characterize energy exchanges among modes. To further assess the system’s dynamic behavior, phase portraits, Poincaré sections, and bifurcation diagrams are employed. These analyses elucidate the onset and evolution of LCOs, offering critical insights into the coupled thermomechanical instabilities of flexible space structures and contributing to the design of more robust spacecraft systems under dynamic thermal environments.